assume data is normally distributed give answers to three de

(assume data is normally distributed, give answers to three decimal places)

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    110      
u = mean =    90      
n = sample size =    45      
s = standard deviation =    23.4      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    5.733507635      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   5.733507635   ) =    4.91873*10^-9 or 0.00000000491873 = 0.000 [ANSWER]